I originally just eyeballed it and guessed 1/9th. It may not sound like much but on something this small it's pretty obvious

I measured the shield a bit and looked at several images to figure out the size of the bird emblem. It'll be 1/8th of an inch wide. It's not as obvious in the first image but the tips of the wings almost perfectly line up with the corners of the grey segments of the shield, the space between those is an 8th of an inch